Question

Find the equation of the parabola with vertex at origin, symmetric with respect to $y-$axis and passing through $(2,-2)$

Answer 1

The vertex of the parabola is at origin and it is symmetric with respect to $y-$axis

Also, it passes through $(2,-2)$ , a point in the fourth quadrant.

Let its equation be $x^2=-4ay$ ........$\left(1\right)$

As it passes through $(2,-2)$, we get

$2^2=-4a\times -2\Rightarrow a=\frac{1}{2}$

Substituting this value of $a$ in $\left(1\right)$, the equation of the parabola is

$x^2=-4\times \frac{1}{2}y$

or $x^2=-2y$